Concept Lattices for Federated Learning Systems

SYLVIA ENCHEVAStord/Haugesund University College

Department HaugesundBjørnsonsg. 45, 5528 Haugesund

NORWAY

SHARIL TUMINUniversity of Bergen

IT-Dept.P. O. Box 7800, 5020 Bergen

NORWAY

Abstract: This paper focuses on a framework for building new courses orupdating existing ones by choosinglearning objects developed at universities that are members of a federated learning system. The aim of this workis twofold. First assisting a lecturer in collecting learning objects closest to the lecturer’s vision on what a subjectshould contain and how the content should be presented. Secondly, present a student with content, tailored accord-ing to student’s individual learning preferences.

Key–Words: Learning objects, concept lattices, federatedsystems

1 Introduction

A variety of learning technology systems and interop-erability standards providing reuse of learning objects(LOs) and interoperability of content across deliveryare developed ([21], [15], and [12]). While most ef-forts aim at providing a technology to access and shareexisting learning objects, there is yet no formal modelof how to filter the most suitable LOs for a subject.

Let us consider a lecturer affiliated with an educa-tional institution that is member of a federated learn-ing system. Suppose the system is able to provide alarge number of LOs upon the lecturer request. A lotof time and efforts can be spared if the system can firstfilter and rank those LOs according to the lecturer’spreferences. Another important issue is how to builda course supporting student’s individual learning pref-erences. The system can help both the lecturer and thestudents by presenting each student with a LO cho-sen from the related set of selected LOs but tailoredaccording to the student’s individual learning stylesand preferences. Identifying a student’s style and thenproviding instruction consistent with that style con-tributes to more effective learning [10].

Our goal is to develop a framework of how to en-able a lecturer to build new courses and/or update ex-isting ones by reusing LOs developed at universitiesthat are members a federated learning system.

The paper is organized as follows. The system’sframework is described in Section 4. Presenting stu-dents with LOs corresponding to learning preferencesis discussed in Section 3. The paper ends with a con-clusion in Section 6.

2 Related Work

SCORM [21] provides technical standards that enableweb-based learning systems to find, import, share,reuse, and export learning content in a standardizedway. However, SCORM is written for toolmakers whoknow what they need to do to their products to con-form with SCORM technically. IEEE Learning Ob-ject Metadata [15] defines a set of resource descriptionframework constructs that facilitates introduction ofeducational metadata into the semantic web. Harve-stRoad Hive [12] is an independent, federated digitalrepository system. It enables the collection, manage-ment, discovery, sharing and reuse of LOs used in thedelivery of online courses within higher education.

Top-down and bottom-up strategies for the devel-opment of tightly coupled, federated information sys-tems are presented in [3]. Information integration,such as intention of treating different kinds of het-erogeneity, preserving source autonomy and enablingchange management while ensuring consistency isfurther discussed.

An agent-oriented method and a generic agent-based architecture for the development of CooperativeInformation Systems (CISs) is presented in [5]. Theproposed method allows mastering the complexity ofthe cooperation processes and the difficulty of settingup effective CISs, by the analysis and the modellingof the cooperation in two levels of abstraction.

A reference model and infrastructure for feder-ated learning content repositories are developed in[18]. It is shown how to provide access to learningcontent, under the base assumption that good learningrequires ubiquitous content, which in turn implies the

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need for an operational content infrastructure.Uncertainties in the database integration process

were analyzed in [1] and [2]. Engineering federatedinformation systems are discussed by many authors,e.g. [9], [14], [14], [19], [20], and [23].

3 Concept Lattices, UnfoldingModel, Learning Styles and Pref-erences

3.1 Concept LatticesA conceptis considered by itsextentand itsintent: theextentconsists of all objects belonging to the conceptwhile theintentis the collection of all attributes sharedby the objects [6].

A contextis a triple (G,M, I) whereG andMare sets andI ⊂ G × M . The elements ofG andMare calledobjectsandattributesrespectively.

ForA ⊆ G andB ⊆ M , define

A′ = {m ∈ M | (∀g ∈ A) gIm},

B′ = {g ∈ G | (∀m ∈ B) gIm}

soA′ is the set of attributes common to all the objectsin A and B′ is the set of objects possessing the at-tributes inB. Then aconceptof the context(G,M, I)is defined to be a pair(A,B) whereA ⊆ G, B ⊆ M ,A′ = B and B′ = A. The extentof the concept(A,B) is A while its intent isB. A subsetA of Gis the extent of some concept if and only ifA′′ = Ain which case the unique concept of the whichA isan extent is(A,A′). The corresponding statement ap-plies to those subsetsB of M which are the intent ofsome concept.

The set of all concepts of the context(G,M, I) isdenoted byB(G,M,I). 〈B(G,M,I);≤〉 is a com-plete lattice and it is known as theconcept latticeofthe context(G,M, I).

For concepts (A1, B1) and (A2, B2) inB(G,M,I) we write (A1, B1) ≤ (A2, B2), andsay that(A1, B1) is asubconceptof (A2, B2), or that(A2, B2) is a superconceptof (A1, B1), if A1 ⊆ A2

which is equivalent toB1 ⊇ B2 [6].

3.2 Unfolding ModelThe unfolding model was devised for the analysis ofranking data based on preferential choice behavior [4].

According to the unidimensional unfoldingmodel, preferential choice is made in the followingmanner: an individual evaluatesm objects based onthe objects’ single common attribute. Each object isrepresented by a real number expressing the level of

this attributexi, i = 1, ...m or a point on the realline R (the ’unidimensional underlying continuum’).Each individual is also represented by a pointy ∈ Ron the same line. The pointy is considered the in-dividual’s favorite and is called the individual’s idealpoint. The real lineR containing both individual’sand objects is thought of as the psychological space.Individuals and objects are identified with their corre-sponding points. The model assumes that individualyranks them objectsxi, i = 1, ...m according to theirdistances fromy, i.e., individualy prefersxi to xj ifand only if |y − xi| < |y − xj|.

3.3 Learning Styles, Orientations and Pref-erences

A learning style is the general, habitual mode of pro-cessing information; it is a predisposition on the partof some students to adopt a particular learning strat-egy regardless of the specific demands of the learningtask: that is, individuals’ learning styles are simply thecognitive styles that they evidence when confrontedwith a learning task [22].

According to Kolb’s model [13], there are fourlearners types - concrete, reflective; abstract, reflec-tive; abstract, active; and concrete, active.

The three learning preferences are auditory(learning by hearing), visual (learning by seeing), andkinesthetic (learning by doing) [7].

3.4 Learning OrientationsStudent learning orientations [16] are critical for indi-vidualizing the instructional process. The system pro-vides different tests with respect to different learningorientations.

Each level has tutorial material generated for it;since it is important to target tutorial tasks at the stu-dent’s ability, this is seen as being of more educationalbenefit than offering the same tutorials to all studentsand then assigning a student to a level based upon thegrade the student achieves [11]. It is incorporated byincluding different help functions. Intelligent agentsprovide different students with different pages accord-ing to their needs. Additional explanations and exam-ples helping to clear current difficulties and miscon-ceptions are provided without use of human tutors.

There are four learning orientations [17]:

• Transforming learners - They placegreat importance on personal strengths, ability,persistent effort, strategies, high-standards, andpositive expectations to self-direct intentionallearning successfully. They prefer loosely struc-tured learning environments.

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• Performing Learners - They are non-risk,skilled learners that consciously, systematically,and capably use cognitive processes, strategies,preferences as they focus on grades and attain-ing normative achievement standards. They pre-fer semi-structured learning environments.

• Comforming Learners - They are compli-ant and more passively accept knowledge, storeit, and reproduce it to conform, complete as-signed tasks if they can, and please others. Theyprefer to have simple standards set for them andreceive explicit guidance and feedback.

• Resistant Learners - They lack a fun-damental belief that academic learning andachievement can help them achieve personalgoals or initiate positive change. These learn-ers do not believe that formal education or aca-demic institutions can be positive or enjoyableinfluences in their life.

4 Framework

The system is based on a flexible framework that pro-vides the instructors and students with possibilities indesigning courses using shared, reusable LOs.

Course design costs a significant part of a WEB-based learning project budget. A big cost reductionis possible if as many LOs as possible are reusableand are shared among collaborative organizations. In-structors can just define which LOs should be in-cluded in their courses. This will make the coursebuilding more flexible and reduce costs for both stu-dents and organizations.

A subject is defined as a strictly sequential list oftopics by a course builder. Each subject definition issaved in the database in XML. The subject’s defini-tion contains all the metadata needed to uniquely de-scribe the subject in question. These metadata includeserver, domain, title, topics list, and other operationalparameters.

A topic is composed of theoretical parts, exer-cises, examples, drills, and assessments, where someof them can be empty. Any of them is a LO designedby expert instructors. These LOs are WEB documents(HTML, PDF, Flash, Java-applet, WEB-form, etc.).

Each topic is defined by the course builder inXML and saved in the database. The topic’s definitioncontains all the metadata needed to describe the topiccontent, drill, and assessment policies. These docu-ments can be used to provide learners with dynamicHTML pages for each invocation of a topic depend-ing on its LO’s set.

Table 1: Context for different universities

(T) (E) (I) (D) (A)U1b × × × ×U1m × ×U1p × × ×U2bU2m × × ×U2p × ×U3bU3m × × ×U3p × × ×

Topics are defined dynamically by diagnosticcomponents of the system. The drills’ design containsinference rules analyzing students’ answers to care-fully prepared tests. Students’ test scores and wrongresponses are used as input parameters to a diagnosticcomponent in the drills, which provides recommen-dations to alternative personal topic trails containingrelevant LOs in order to solve the current topic’s drill.

Assessments are used for both formative andsummative evaluations. Exercises give a list of un-solved problems for students to practice on, while ex-amples can be a list of solved problems, Flash, orJava-applets for students to work with. Since eachLO is self-contained, they can be developed indepen-dently at different organizations. Expert instructors ateach organization maintain a repository of LOs. Forstudents at different collaborative organizations, theywill have the advantage that all LOs are accessible tothem. For organizations owning the LOs, an audit trailfor each LO can easily be gathered for billing pur-poses.

For the sake of simplicity we limit the amount ofuniversities, study programs and related attributes tothe ones included in Table 1.

The abbreviated objects are -University 1 Bachelor level (U1b),University 1 Master level (U1m),University 1 PhD level (U1p),University 2 Bachelor level (U2b),University 2 Master level (U2m),University 2 PhD level (U2p),University 3 Bachelor level (U3b),University 3 Master level (U3m),University 3 PhD level (U3p).

The abbreviated attributes are -Theory (T) - HTML, PDF, Flash, Java-applet,

WEB-formExercises (E) - HTML, PDF, Flash

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Figure 1: Hasse-diagram for different universities

Interactive examples (I) - Flash, Java-appletDrills (D) - WEB-formAssessment (A) - WEB-form.

The corresponding concept lattice is shown inFig. 1.

5 System Architecture

The framework is composed of base system, runtimesupport, and agents.

Base SystemApache is used as a Web server with a Python in-

terpreter extention using a mod−python module. Post-greSQL is used as a relational database that supportsStructured Query Language (SQL).

Python is an object-oriented scripting language.Having a Python interpreter module in the Web serverincreases performance and reduces response time sig-nificantly. A standard Apache implementation withCommon Gateway Interface (CGI) scripts can also beused. However, this will lead to a performance penaltyin that the Web server needs to start a new externalPython interpreter each time a CGI script is called.

A relational database management system is usedto store tests and students’ data. PostgreSQL pro-vides us with database support for flexible implemen-tation. All data is stored in a relational database andcan be queried programmatically by Python scripts us-ing SQL. Other relational databases such as MySQL

and Oracle can be used instead. We have developedcontents of learning materials on a Linux workstation.

Runtime supportDynamic HTML pages are created by server-side

scripts written in Python. Python programs are alsoused for database integration, diagnostics, and com-munication modules.

AgentsThe system is supported by student profile, test,

and diagnostic agents which we will discuss further inthis paper.

The system structure is defined by pedagogicalrequirements. This structure defines dependenciesamong learning materials, levels and relationships be-tween tests options, and inference rules used in adi-agnostic agent. This structure is crucial in providingeach student with a personalized learning work-flowfor efficient learning. The system provides differentstudents with different pages according to their needs.The responses from each student to the suggestionsfrom the system provide thediagnostic agent withnecessary data. Thediagnostic agent analyzes thesedata using the programmed inference rules and pro-vides the student with an immediate recommendationon how to proceed. The student status is saved in thedatabase.

It is based on each individual’s learning styles,orientations and preferences, and chooses the most ap-propriate LOs for the course, (see Fig.2). The selec-tion process was discussed in Section 4. An agent isfirst checking whether all definitions and statementsrequired are included in the suggested LOs. Anotheragent determines whether the level of difficulties as-sumed for the new LOs corresponds to the level of dif-ficulties of the suggested LOs. The unfolding model(shortest distance) (see 3.2) is used while comparingdifferent LOs. The level of difficulties is judged basedon the included theory, examples and assessment tests.

A questionnaire is put to the students for deter-mining their individual learning preferences (see 3.3).In the recommendation on how to proceed, a studentcan choose to subscribe to one or more suggestedlearning materials. The student’s learning materialsubscriptions are placed in a stack-like structure inthe student profile data. Thestudent profile agentpresents the student with the top most learning mate-rial in the profile stack for each new learning session.

Initially, the profile stack contains a sequential or-dering of learning materials in a given subject. A stu-dent can choose to skip any presented learning mate-rial and go to the next one at any time. A student isconsidered to have completed a course when his/herprofile stack is empty and he/she has passed all com-pulsory tests assigned to the course.

All learning material names taken by the student

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Diagnostic Agent

Database

Dinamic Page

Publisher

Serversidescript

Test Agent

StudentProfileAgent

UsersStack

Profiler

Agents

Supporting Subsystem

SelectedLOs

LearningMaterials

Internet

Web Server

Figure 2: System architecture

during the course and scores of the tests are saved inthe student audit-trail. Such audit-trail data is used forbilling purposes while global analysis of the courseand feedback data is used to improve learning materi-als for each subject.

The server-side script (SSS) contains studentand teacher modules. The student module contains,among other things, student registration, student ad-ministration, student authentication, and authoriza-tion. The teacher module provides an interface for ateacher to define topics and subjects, students’ statusreports/diagnostic, and messaging.

SSS modules and agents communicate with eachother by a request-respond mechanism in which re-mote procedure calls are done among different mod-ules/agents providing students with a dynamic andpersonalized learning environment.

A pedagogically crafted scheme with a set ofquestions and answers provides atest agent with aprogrammed intelligence, in which wrong answers toa drill lead learners to appropriate hints and examples.The students can then subscribe to those learning ma-terials suggested by the hints or try the drill again andcontinue with the current course. Students can jumpback to the current course trail at any time while fol-lowing trails suggested by thetest agent. The agentcalculates scores, shows result status, and keeps trackof assessments taken by each student. After each as-sessment thetest agent sends summarized informa-tion to thediagnostic agent.

5.1 Supporting SubsystemStack Profiler

In the recommendation on how to proceed, a stu-dent can choose to subscribe to one or more suggestedLOs. The student’s LO subscriptions are placed in astack-like structure in the student profile data. Thesystem presents the student with the top most LO ineach new learning session.

Initially, the profile stack contains a sequential or-dering of LOs in a given subject. A student can chooseto skip any presented LOs and go to the next one atany time. A student is considered to have completed acourse when her/his profile stack is empty and she/hehas passed all compulsory tests assigned to the course.

All element names taken by the user during thecourse and scores of the tests are saved in the useraudit-trail. Such audit-trail data is used for billing pur-poses while global analysis of the course and feedbackdata is used to improve contents and tests for each sub-ject.

PolicyThe curriculum of each subject at every uni-

versity should be described using a set of agreedupon metadata presented in a standard structure ina database, for example a name space of a LO in adatabase.University:Faculty:Level:Course-name:Learning-object:Expire-data

LO Caching- If LOs in a course are connected with hyper-

links, the course builder risks to end up with somedead links during the semester.

- If all LOs in a course are cached on a localserver, the course builder is sure that all LOs are go-ing to be available to the students through the entiresemester. The owners of the LOs have no control overthe amount of students and number of times those LOsare used. However, the owners of the LOs can in-clude f. ex. 1×1 pixel gif picture in every LO. Thusthe owners will get information from log files for thenumber of times a LO has been used and by how manydifferent users.

6 ConclusionThis paper describes a framework for building newcourses or updating existing ones by choosing learn-ing objects developed at universities that are membersa federated learning system. The proposed system hasbeen exploited by four high level educational institu-tions. Both course builders and students expressedsatisfaction using it. Eventhough LOs are indexedwith metadata which simplifies the process of iden-tifying, locating and retrieving them, additional work

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is needed for further improvement of the automatedselection of LOs.

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